312414865920 has 640 divisors, whose sum is σ = 1219036262400. Its totient is φ = 75487002624.

The previous prime is 312414865879. The next prime is 312414865927. The reversal of 312414865920 is 29568414213.

312414865920 is a `hidden beast` number, since 3 + 12 + 4 + 1 + 48 + 6 + 592 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (640).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (312414865927) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 30200269 + ... + 30210611.

It is an arithmetic number, because the mean of its divisors is an integer number (1904744160).

Almost surely, 2^312414865920 is an apocalyptic number.

312414865920 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 312414865920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (609518131200).

312414865920 is an abundant number, since it is smaller than the sum of its proper divisors (906621396480).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

312414865920 is a wasteful number, since it uses less digits than its factorization.

312414865920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10417 (or 10395 counting only the distinct ones).

The product of its (nonzero) digits is 414720, while the sum is 45.

The spelling of 312414865920 in words is "three hundred twelve billion, four hundred fourteen million, eight hundred sixty-five thousand, nine hundred twenty".